Flourishing programs in 90+ disciplines. A vibrant Christian mission. $50 million
in new campus construction. Championship athletics. 94% placement within 6 months
of graduation. There’s never been a better time to consider Hope College.

As a member of the MIAA and NCAA Division III associations, Hope College sponsors
22 varsity sports for men and women. The college is home to the 2014 NCAA Division
III National Championship women’s volleyball team.

Breadcrumb Navigation

Todd Swanson of the Hope College mathematics faculty has co-authored the textbook
“A Spiral Approach to Financial Mathematics,” offering a new way of learning the concepts.

The book is being published in July by Academic Press, an imprint of Elsevier. An
associate professor of mathematics, Swanson wrote the book with Dr. Nathan Tintle
of the Dordt College mathematics and statistics faculty, and Nathan Schelhaas, an
actuary with Principal Financial Group of Des Moines, Iowa.

The term “spiral” refers to the way that the material has been organized. “A Spiral
Approach to Financial Mathematics” begins by introducing key concepts, which are then
referenced and built upon throughout as the book goes into greater depth. Chapter
topics include savings, loans, annuities, stocks and bonds, and portfolios.

“The traditional approach to teaching FM starts with simple, unrealistic financial
situations, with an emphasis on formulas and computation,” the authors note in their
preface.

“Alternatively, we start with practical, conceptual problems for which students have
a good intuition,” they continue. “For example, while an amortized loan has a challenging
formula, the key concepts (e.g., payback must include interest plus principal; the
larger the payment the quicker the loan is paid off) are relatively straightforward
and intuitive.”

Reviewer Dr. Donna Fengya of William Paterson University praised “A Spiral Approach
to Financial Mathematics,” stating, “This book provides a practical, conceptually
focused, and dare might I say, revolutionary approach to the coverage of Financial
Mathematics. What makes the authors’ approach unique is that standard topics are
first presented in a manner appropriate for students without a calculus background,
and are later revisited to provide a complete and thorough coverage for more mathematically
advanced students. Excel examples are masterfully included in every chapter to encourage
students to explore a variety of topics which enhances intuitive feel and understanding
of underlying concepts.”

The book is divided into two units. The first unit is geared toward students who
wish to gain a solid mathematical foundation with which to inform their future personal
and professional financial decision making. The second unit provides more technical
and detailed concepts for students who hope to pass the financial mathematics examination
required for actuarial certification.

The authors modeled their approach on the Guidelines for Assessment and Instruction
in Statistics Education published by the American Statistical Association in 2007.
The ASA calls for instructors to emphasize statistical literacy and develop statistical
thinking, use real data, stress conceptual understanding rather than mere knowledge
of procedures, foster active learning in the classroom, use technology for developing
conceptual understanding and analyzing data, and use assessments to improve and evaluate
student learning. Swanson and Tintle had applied the guidelines in the 2015 book
“Introduction to Statistical Investigations,” which they co-authored with Jill VanderStoep
an adjunct assistant professor of mathematics at Hope; Dr. Beth Chance of California
Polytechnic State University; Dr. George Cobb, an emeritus member of the Mount Holyoke
College faculty; Dr. Allan Rossman of California Polytechnic State University; and
Dr. Soma Roy of California Polytechnic University.

Related News

Emily St. John Mandel, author of “Station Eleven,” the novel being featured during this year’s NEA Big Read Lakeshore, will discuss her work during a keynote presentation on Tuesday, Nov. 13, at 7 p.m. in the Concert Hall of the Jack H. Miller Center for Musical Arts.

Nobel Prize-winning chemist Dr. Peter Agre of the Johns Hopkins School of Public Health will deliver two addresses while at Hope College on Thursday and Friday, Feb. 1 and 2, through the college’s Gentile Interdisciplinary Lecture series in the natural and applied sciences.

“We really needed something to cheer for right now. We needed some positivity. We needed a good headline that could carry the day,” says Daryl Van Tongeren, associate professor of psychology, who studies how humans build meaning in their lives.